Question

Пря­мая, па­рал­лель­ная сто­ро­не AC тре­уголь­ни­ка ABC, пе­ре­се­ка­ет сто­ро­ны AB и BC в точ­ках M и N со­от­вет­ствен­но. Най­ди­те BN, если MN = 13, AC = 65, NC = 28.Желательно с фоткой или подробно

Answer 1

Так как отрезок MN параллелен стороне AC и пересекает стороны треугольника AB и BC, то углы, прилежащие к отрезку MN и к стороне треугольника AC равны- это признак подобия двух треугольников: ABC и MBN.
AC/MN=65/13=5/ Отношение треугольника MBN к ABC= 1/5, так как треугольники подобны, то между их сторонами такое же отношение 1 к 5.
Чтобы найти сторону, нужно BC/5  BC-? Найдём с помощью уравнения:
Пусть "x"= длине BC, тогда MN="x/5", так как остальная часть равна 28, то уравнение будет таким:
x/5+28=x;
Приведя уравнение к общему знаменателю "5", оно будет таким:
(x+28*5)/5=5x; От знаменателя можно избавится
x+140=5x;   4x=140;   x=140/4=35.
35/5=7 длина BN.
Ответ: BN=7.

Answer 2

Finding BN in Triangle ABC

To find the length of BN in triangle ABC, we can use the given information that MN = 13, AC = 65, and NC = 28.

Let's break down the problem step by step:

1. We know that MN is parallel to AC and intersects sides AB and BC at points M and N, respectively. This implies that triangles AMN and ABC are similar triangles.

2. Using the concept of similar triangles, we can set up the following proportion:

AB / AM = BC / AN

Since we are interested in finding BN, we rearrange the proportion as follows:

AN / AB = BC / BN

3. We are given that MN = 13, AC = 65, and NC = 28. Using these values, we can find the lengths of AM and AN:

AM = AC - CM = 65 - 28 = 37

AN = AC - CN = 65 - 28 = 37

4. Now, we can substitute the values of AM, AN, and BC into the proportion from step 2:

37 / AB = BC / BN

5. To solve for BN, we need to find the value of AB. We can use the Pythagorean theorem to find AB:

AB^2 = AM^2 + BM^2

Since we don't have the value of BM, we need to find it using the given information. We know that MN is parallel to AC, so triangles AMN and ABC are similar. This means that the ratio of corresponding sides is equal:

MN / AC = AN / AB

Substituting the given values:

13 / 65 = 37 / AB

Solving for AB:

AB = (65 * 37) / 13 = 185

6. Now that we have the value of AB, we can substitute it into the proportion from step 4:

37 / 185 = BC / BN

Solving for BN:

BN = (BC * 185) / 37

7. However, we still need to find the value of BC. Unfortunately, the given information does not provide the length of BC. Without this information, we cannot determine the exact value of BN.

Therefore, without the length of BC, we cannot find the exact value of BN.